When zero doesn't mean it and other geomathematical mischief

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There is almost not a case in exploration geology, where the studied data doesn’t
includes below detection limits and/or zero values, and since most of the geological data
responds to lognormal distributions, these “zero data” represent a mathematical
challenge for the interpretation.
We need to start by recognizing that there are zero values in geology. For example the
amount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-exists
with nepheline. Another common essential zero is a North azimuth, however we can
always change that zero for the value of 360°. These are known as “Essential zeros”, but
what can we do with “Rounded zeros” that are the result of below the detection limit of
the equipment?
Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes
we need to differentiate between a sodic and a potassic alteration. Pre-classification into
groups requires a good knowledge of the distribution of the data and the geochemical
characteristics of the groups which is not always available. Considering the zero values
equal to the limit of detection of the used equipment will generate spurious
distributions, especially in ternary diagrams. Same situation will occur if we replace the
zero values by a small amount using non-parametric or parametric techniques
(imputation).
The method that we are proposing takes into consideration the well known relationships
between some elements. For example, in copper porphyry deposits, there is always a
good direct correlation between the copper values and the molybdenum ones, but while
copper will always be above the limit of detection, many of the molybdenum values will
be “rounded zeros”. So, we will take the lower quartile of the real molybdenum values
and establish a regression equation with copper, and then we will estimate the
“rounded” zero values of molybdenum by their corresponding copper values.
The method could be applied to any type of data, provided we establish first their
correlation dependency.
One of the main advantages of this method is that we do not obtain a fixed value for the
“rounded zeros”, but one that depends on the value of the other variable.
Key words: compositional data analysis, treatment of zeros, essential zeros, rounded
zeros, correlation dependency
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